Logistic type equations on RN by a squeezing method involving boundary blow-up solutions

We study, on the entire space RN(N≥1), the diffusive logistic equationut–∆u=λu–up, u≥0 (1.1)and its generalizations. Here p > 1 is a constant. Problem (1.1) plays an important role in understanding various population models and some other problems in applied mathematics. When λ = 1 and p = 2, it is also known as the Fisher equation and KPP equation, due to the pioneering works of Fisher [8] and Kolmogoroff, Petrovsky and Piscounoff [18].